Off-state breakdown voltage, Vbr, is an important parameter determining the maximum power output of microwave Field Effect Transistors (FETs). In recent years, the use of field plates has been widely adopted to significantly increase Vbr. This important technological development has extended FET technologies into new areas requiring these higher voltages and power levels. Keeping with this goal, field plates were added to an existing AlGaAs / InGaAs pseudomorphic High Electron Mobility Transistor (pHEMT) process with the aim of determining the off-state breakdown mechanism and the dependency of Vbr on the field plate design. To find the mechanism responsible for breakdown, temperature dependent off-state breakdown measurements were conducted. It was found that at low current levels, the temperature dependence indicates thermionic field emission at the Schottky gate and at higher current levels, impact ionization is indicated. The combined results imply that impact ionization is ultimately the mechanism that is responsible for the breakdown in the tested transistors, but that it is preceded by thermionic field emission from the gate. To test the dependence of Vbr upon the field plate design, the field plate length and the etch depth through the highly-doped cap layer under the field plate were varied. Also, non-field plate devices were tested along side field plate transistors. It was found that the length of the etched region under the field plate is the dominant factor in determining the off-state breakdown of the more deeply etched devices. For less deeply etched devices, the length of the field plate is more influential. The influence of surface states between the highly doped cap layer and the passivation layer along the recess are believed to have a significant influence in the case of the more deeply etched examples. It is believed that these traps spread the electric field, thus raising the breakdown voltage. Three terminal breakdown voltages approaching 60V for the most deeply recessed devices are seen.